Determination of subencoding MRI coil sensitivities in a lower order magnetic field

ABSTRACT

A novel magnetic resonance imaging method is presented for forming an image of an object from a plurality of signals acquired by an array of receiver antennae, whereas prior to imaging a sensitivity map of each of the receiver antennae is provided, at least two adjacent antennae record signals originating from the same imaging position and the image intensity is calculated from the signals measured by different antennae, wherein the number of phase encoding steps is reduced with respect to the full set thereof. Further the homogeneity of the main magnetic field is defined in a first region of full homogeneity, a second region of moderate homogeneity and a third region of full inhomogeneity, the sensitivity data of the array of receiver antennae is measured by a coarse calibration scan, whereas the full measured sensitivity data is used in the first region, for each point in the second region an estimate of the coil sensitivities is derived by a weighted addition of the measured sensitivities in the neighborhood of that point, and in the third region the sensitivity data is set zero.

FIELD OF THE INVENTION

The invention relates to a magnetic resonance (MR) method for theimaging of an object from a plurality of signals acquired by an array ofreceiver antennae, whereas prior to imaging a sensitivity map of each ofthe receiver antennae is provided, at least tow adjacent antennae recordsignals originating from the same imaging position and the imageintensity is calculated from the signals measured by the differentantennae, and wherein the number of phase encoding steps is reduced withrespect to the full set thereof.

The invention also relates to an MR device and a computer programproduct for carrying out such a method.

BACKGROUND OF THE INVENTION

In magnetic resonance imaging there is a general tendency to obtainacceptable images within shorter periods of time. For this reason thesensitivity encoding method called “SENSE” has recently been developedby the Institute of Biomedical Engineering and Medical Informatics,University and ETH Zürich, Switzerland. The SENSE method is based on analgorithm which acts directly on the image as detected by the coils ofthe magnetic resonance apparatus and in which subsequent encoding stepscan be skipped and hence an acceleration of the signal acquisition forimaging by a factor of from two to three can be obtained. Crucial forthe SENSE method is the knowledge of the sensitivity of the coilsarranged in so called sensitivity maps. In order to accelerate thismethod there are proposals to use raw sensitivity maps which can beobtained through division by either the “sum-of-squares” of the singlecoil references or by an optional body coil reference (see e.g. K.Pruessmann et. al. in Proc. ISMRM, 1998, abstracts pp. 579, 799, 803 and2087). In fact the SENSE method allows for a decrease in scan time bydeliberately undersampling k-space, i.e. deliberately selecting aField-of-View (FOV) that is smaller than the object to be acquired. Fromthis undersampling fold-over artefacts are obtained which can beresolved or unfolded by the use of the knowledge of a set of distinctcoils having different coil sensitivity patterns. The undersampling canbe in either one of both phase-encoding directions.

It is commonly known that the main magnet of the Philips NT with theIntera 1.5 T magnet (Philips Medical Systems, Best, Netherlands) has aquit sharp distinction between the inner region in which the mainmagnetic field is homogeneous and the outer region in which the mainmagnetic field is completely inhomogeneous. For the Intera 1.5 T magnetthe inner region of high homogeneity is larger than the usual extent ofthe human body in the left-to-right direction which is orthogonal to theelongate direction of the magnet. The polynomial expansion of the mainmagnetic field is zero up to a high-order, which means that there is aquick transition between the inner region or volume of high homogeneityand the outer region of high inhomogeneity.

Other known MR systems have another design of their main magnets, whichhave a more gradual transition between the high homogeneity region andthe region in which the main magnetic field is completely inhomogeneous,i.e. where fields are not sufficient homogeneous for any RF refocusingwhatsoever. Such magnets are being mentioned here as of “lower order”.

For the set-up of SENSE it is required to provide a sensitivity map ofthe coils which is done by means of a large voxel gradient echo imagingor fast field echo scan (FFE), which is also known as coarse calibrationscan (COCA). This scan is sensitive to signal loss due to intra-voxeldephasing in case of moderate magnetic field inhomogeneities. For thisreason up to now the SENSE method is practically only feasible with thePhilips MR system because of the high homogeneity of the main magneticfield.

In U.S. Pat. No. 5,910,728 a magnetic resonance imaging apparatus andtechnique exploits spatial information inherent in a surface coil arrayto increase MR image acquisition speed, resolution and/or field of view.The MR signal from a combination of coils having an aggregate sinusoidaland cosinusoidal spatial sensitivity profile have an information contentsomewhat different from that of the usual coil signal. By separating outone or more collected signals corresponding to pure spatial harmonics,these may be used to fill a larger portion of the data space than isdone conventionally. Partial signals are thus acquired simultaneously inthe component coils of the array and formed into two or more signalscorresponding to orthogonal spatial representations. In a Fourierembodiment, lines of the k-space matrix required for image productionare formed using a set of separate linear combinations of the componentcoil signals to substitute for spatial modulations normally produced byphase encoding gradients. The combined MR signal from the inhomogeneouscoils is thus shifted in k-space by a predetermined amount dependentfrom the spatial frequency of the inhomogeneous coil sensitivity. Thisk-space shift has precisely the same form as the phase-encoding shiftproduced by evolution in a y gradient. This method is specificallydesigned for SMASH. However, it does not give any further indication tosolve the problem of using SENSE with designs of main magnet of lowerorder as discussed above.

It is an object of the present invention to allow the application ofSENSE with a main magnet with a more gradual transition between theregion with a homogeneous magnetic field and the region with ainhomogeneous magnetic field, i.e. with magnets of lower order.

This object of the invention are achieved by a method as defined inclaim 1. The invention is further related to an apparatus as defined inclaim 6 and to a computer program product as defined in claim 7.

The present invention has the main advantage that main magnets with aless sharp distinction between the inner region of high homogeneity andthe outer region of complete inhomogeneity, i.e. magnets of lower order,now can be used also for the above mentioned SENSE method.

These and other advantages of the invention are disclosed in thedependent claims and in the following description in which anexemplified embodiment of the invention is described with respect to theaccompanying drawings. Therein shows:

DETAILED DESCRIPTION OF THE DRAWING

FIG. 1 an MR image of a patient with an interesting organ, and

FIG. 2 an MR imaging system for carrying out the method of the presentinvention.

DESCRIPTION OF THE PREFERRED EMBODIMENT

In the present description, a distinction is made between “homogenous”and “inhomogeneous” magnetic fields. In practical terms commercialavailable magnet systems do not provide an absolutely homogenousmagnetic field. However, the Intera 1.5 T magnet of Philips MedicalSystems, Best, Netherlands differentiates from a variety of magnets ofother systems in the following important aspects.

-   -   The region of high homogeneity is relatively large; in        particular, it is larger than the usual extent of the human body        in left/right direction.    -   The polynomial expansion of the field is zero up to a        high-order, which means that, colloquially, there is a quick        transition between “very homogeneous” within the “homogeneity        volume”, and “very inhomogeneous” outside.        Many other magnet designs, which are called here of “lower        order”, have a more gradual transition between a region of high        homogeneity and the completely inhomogeneous region, where        fields are too inhomogeneous in order to refocus any MR-signal        yet. If there is no magnetic field anymore

In parallel imaging, such as SENSE, SMASH etc. undersampling of theMR-signals in k-space is employed. That is, the number of (phase)encoding steps is reduced with respect to a full set of encoding steps.This full set induces the encoding steps required for samplingMR-signals in k-space sufficient for a pre-selected spatial resolutionof the MR-image that is reconstructed.

As has been described before, in the SENSE set-up reference data isacquired using a large-voxel FFE scan (the so-called “COCA” scan). Thisis sensitive to signal-loss due to intra-voxel dephasing in case ofmoderate magnetic-field inhomogeneities.

On the contrary, there are many types of scans for which in principleSENSE could be used but the scans themselves are much less sensitive toinhomogeneities and thus normally SENSE cannot be applied. RF-refocusedscans (SE and particularly TSE) fall in that category, but also short TEscans with small voxels.

In FIG. 1 a normal slice of an MR image of a patient 15 with aninteresting organ 16 (the heart) with his arms 17 alongside him ispresented in thick lines. The dashed line 18 represents the edge of afirst region of high homogeneity of the main magnet, so outside thisregion the reference or coarse calibration (“COCA”) scan shows nomeaningful coil-sensitivity information due to dephasing. Outside thedotted line 19, which defines a third region, the inhomogeneity of themagnet system is such high that no sensible signals can be collected. Ifthe magnetic field is vanishing to zero, it is per definition also fullyinhomogeneous. A second region 20 between dashed line 18 and the dottedline 19 is of moderate inhomogeneity, i.e. the region within which theSENSE-scan is still able to collect any meaningful signal. The marginbetween the dashed line 18 and the dotted line 19 is typically about 20mm wide. The problem area is the intermediate region 20, in which animage is performed by the SENSE-scan and which is possibly folded overan interesting region. However, the reference scan cannot reveal it andhence the system has no knowledge on coil-sensitivities in that region.This results in bad SENSE-unfolding, i.e. artefacts.

The system is designed in such a way that knowledge on expected fieldinhomogeneities (or their variations) are explicitly known for alllocations within the magnet bore. From that knowledge (and knowing theproperties of the COCA scan), a figure indicating the “reliability ofsensitivity information” can be derived for every point within themagnet bore.

In the COCA scan, the sensitivity information is measured. In thehigh-homogeneity region it is accurate but elsewhere it is not. Theknowledge on where this information is reliable allows for anextrapolation scheme which consists of the following smoothingalgorithm: on each position, i.e. point, an estimate of coilsensitivities is derived by a weighted addition of the measuredsensitivities of the region around that point; the weights depend on

-   a) The distance between the point and points in its direct    neighborhood.-   b) The reliability of the information at neighboring points.    Formally, this may be written as

$\begin{matrix}{{{\hat{S}}_{c}\left( {x,y,z} \right)} = \frac{\sum\limits_{{({i,j,k})}\varepsilon\;{{Region}{({x,y,z})}}}{{S_{c}\left( {i,j,k} \right)} \cdot {r\left( {i,j,k} \right)} \cdot {D\left( {{x - i},{x - j},{z - k}} \right)}}}{\sum\limits_{{({i,j,k})}\varepsilon\;{{Region}{({x,y,z})}}}{r{\left( {i,j,k} \right) \cdot {D\left( {{x - i},{x - j},{z - k}} \right)}}}}} & (1)\end{matrix}$where ŝ_(c)(x, y, z) is the estimate of sensitivity of coil c atposition (x, y, z); the measured value of coil sensitivity is s. Thefunction D is a monotonically decreasing function of distance (e.g.(distance+constant)^(−p), with the power p preferably larger than 2).The reliability function r is derived from the knowledge of the fieldinhomogeneity; more specifically, it is preferably a function that is 1in case of high homogeneity and 0 in regions with high inhomogeneity,e.g.,

$\begin{matrix}{r = {\mathbb{e}}^{- \frac{{{{grad}{(B)}}}^{2}}{{grad\_ ref}^{2}}}} & (2)\end{matrix}$where “grad_ref” is a constant that is chosen in accordance with theproperties of the the COCA scan.

In order to apply magnet systems with a higher degree of inhomogeneity,i.e. magnets of lower order, the estimated sensitivities ŝ are ratherused than the measured sensitivities s when reconstructing SENSE-imagesin the region of moderate inhomogeneity.

A practical embodiment of an MR device is shown in FIG. 2, whichincludes a first magnet system 2 for generating a steady magnetic field,and also means for generating additional magnetic fields having agradient in the X, Y, Z directions, which means are known as gradientcoils 3. The Z direction of the co-ordinate system shown corresponds tothe direction of the steady magnetic field in the magnet system 2 byconvention, which only should be linear. The measuring co-ordinatesystem x, y, z to be used can be chosen independently of the X, Y, Zsystem shown in FIG. 2. The gradient coils 3 are fed by a power supplyunit 4. An RF transmitter coil 5 serves to generate RF magnetic fieldsand is connected to an RF transmitter and modulator 6. A receiver coilis used to receive the magnetic resonance signal generated by the RFfield in the object 7 to be examined, for example a human or animalbody. This coil 5 represents an array of multiple receiver antennae.Furthermore, the magnet system 2 encloses an examination space which islarge enough to accommodate a part of the body 7 to be examined. The RFcoil 5 is arranged around or on the part of the body 7 to be examined inthis examination space. The RF transmitter coil 5 is connected to asignal amplifier and demodulation unit 10 via a transmission/receptioncircuit 9. The control unit 11 controls the RF transmitter and modulator6 and the power supply unit 4 so as to generate special pulse sequenceswhich contain RF pulses and gradients. The control unit 11 also controlsdetection of the MR signal(s), whose phase and amplitude obtained fromthe demodulation unit 10 are applied to a processing unit 12. Thecontrol unit 11 and the respective receiver coils 3 and 5 are equippedwith control means to enable switching between their detection pathwayson a sub-repetition time basis (i.e. typically less than 10 ms). Thesemeans comprise inter alia a current/voltage stabilization unit to ensurereliable phase behavior of the antennae, and one or more switches andanalogue-to-digital converters in the signal path between coil andprocessing unit 12. The processing unit 12 processes the presentedsignal values so as to form an image by transformation. This image canbe visualized, for example by means of a monitor 13.

1. A magnetic resonance imaging method for forming an image of an objectfrom a plurality of signals acquired by an array of receiver antennae, asensitivity map of each of the receiver antennae being provided, and anumber of applied encoding steps being reduced with respect to the fullset thereof, wherein the homogeneity of the main magnetic field isspecified in a first region of full homogeneity, a second region ofmoderate homogeneity and a third region of full inhomogeneity, and thatthe sensitivity data of the array of receiver antennae is measured by acoarse calibration scan, wherein the full measured sensitivity data isused in the first region, for positions in the second region an estimateof the coil sensitivities is derived by a weighted addition of themeasured sensitivities in the neighborhood of the position at issue, andin the third region the sensitivity data is set to zero.
 2. A method asclaimed in claim 1, wherein weighting for the position at issue dependson the distance between the points at issue of the second region andpositions in its neighborhood and depends on a reliability function ofthe data obtained at those neighboring points.
 3. A method as claimed inclaim 2, wherein the estimate of the sensitivity of a coil (c) at aposition (x, y, z) is defined by following equation:${{\hat{s}}_{c}\left( {x,y,z} \right)} = \frac{\sum\limits_{{({i,j,k})} \in {{Region}{({x,y,z})}}}\;{{s_{c}\left( {i,j,k} \right)} \cdot {r\left( {i,j,k} \right)} \cdot {D\left( {{x - i},{x - j},{z - k}} \right)}}}{\sum\limits_{{({i,j,k})} \in {{Region}{({x,y,z})}}}\;{{r\left( {i,j,k} \right)} \cdot {D\left( {{x - i},{x - j},{z - k}} \right)}}}$wherein ŝ_(c)(x, y, z) is the estimate of sensitivity of coil c atposition (x, y, z); s is the measured value of coil sensitivity; r is areliability function and D is a monotonically decreasing function of thedistance between the point and its neighboring points.
 4. A method asclaimed in claim 3, wherein the reliability function is derived from theknowledge of the inhomogeneity of the main magnetic field.
 5. A methodas claimed in claim 4, wherein the reliability function$r = {\mathbb{e}}^{- \frac{{{{grad}{(B)}}}^{2}}{{grad\_ ref}^{2}}}$where “grad_ref” is a constant that is determined by the properties ofthe coarse calibration scan.
 6. A magnetic resonance imaging apparatusfor obtaining an MR image from a plurality of signals comprising: meansfor excitation of spins in a part of the object, a plurality of receiverantennae, means for measuring MR signals along a predeterminedtrajectory containing a plurality of lines in k-space by application ofa read gradient and other gradients, wherein a number of phase encodingsteps applied is reduced with respect to the full set thereof, means formeasuring sensitivity data for each of the receiver antennae by a coarsecalibration scan, means for specifying the homogeneity of the mainmagnetic field in a first region of full homogeneity, a second region ofmoderate homogeneity and a third region of full inhomogeneity, thesensitivity data of the array of receiver antennae is measured by acoarse calibration scan with reference data, means for deriving anestimate of the coil sensitivities for positions in the second region bya weighted addition of the measured sensitivities in the neighborhood ofthe position at issue, and means for setting the sensitivity data in thethird region to zero.
 7. A computer readable medium having a storedcomputer program comprising the step of: measuring sensitivity data foreach of the receiver antennae by a coarse calibration scan withreference data, specifying the homogeneity of the main magnetic field ina first region of full homogeneity, a second region of moderatehomogeneity and a third region of full inhomogeneity, the sensitivitydata of the array of receiver antennae is measured by a coarsecalibration scan, deriving an estimate of the coil sensitivities forpositions in the second region by a weighted addition of the measuredsensitivities in the neighborhood of the position at issue, and settingthe sensitivity data in the third region to zero.